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Question Number 144787 Answers: 1 Comments: 0

Q :: # Calculus # If : 𝛗 ( n ) : = ∫_0 ^( 1) (( x^( 2n) )/(1 + x^( 2) )) dx then find the value of :: S := Σ_(n=1) ^∞ ((( −1 )^( n) 𝛗 ( n ))/n) = ? m.n.july.1970

$You can't use 'macro parameter character #' in math mode$ $If : ϕ (n) : = \int_{0}^{1} \frac{x^{2 n}}{1 + x^{2}} d x$ $then find the value of ::$ $S := \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n} ϕ (n)}{n} = ?$ $m . n . july . 1970$

Question Number 144782 Answers: 0 Comments: 0

Question Number 144771 Answers: 0 Comments: 0

A region is enclosed by curves x^2 =4y, x^2 =−4y, x=4 & x=−4 V_1 is the volume of the solid obtained by rotating the above region round the y−axis. Another regions consists of points (x,y) satisfying x^2 +y^2 ≤16, x^2 +(y−2)^2 ≥4 and x^2 +(y+2)^2 ≥4 ,V_2 is the volume of the solid obtained by rotating this region round the y−axis Then V_1 =...

$A region is enclosed by curves$ $x^{2} = 4 y, x^{2} = - 4 y, x = 4 & x = - 4$ $V_{1} is the volume of the solid obtained$ $by rotating the above region round$ $the y - axis . Another regions$ $consists of points (x, y) satisfying$ $x^{2} + y^{2} ⩽ 16, x^{2} + {(y - 2)}^{2} ⩾ 4 and$ $x^{2} + {(y + 2)}^{2} ⩾ 4, V_{2} is the volume$ $of the solid obtained by rotating$ $this region round the y - axis$ $Then V_{1} = . . .$

Question Number 144764 Answers: 1 Comments: 0

Question Number 144763 Answers: 0 Comments: 0

Question Number 144756 Answers: 1 Comments: 1

Question Number 144738 Answers: 1 Comments: 0

On souhaite calculer I=∫_0 ^∞ ((sint)/t)dt. (1) On de^ finit la fonction F(x)=∫_0 ^∞ e^(−tx) ((sint)/t)dt. (a) De^ terminer le domaine de de^ finition de f sur R. (b) Montrer que F est de classe C^1 sur R_+ ^∗ et calculer F ′(x). (c) Limite de F en +∞ ? Conse^ quence ? (2) On note Si(t)=∫_0 ^t ((sinu)/u)du pour tout re^ el t. (a) Montrer que G(x)=∫_0 ^∞ e^(−tx) Si(t)dt est de^ finie sur R_+ ^∗ . (b) Montrer que xG(x)→I quand x→0^+ . (c) Au moyen d′une inte^ gration par parties, montrer que F est continue en 0. (3) Calculer I.

$On souhaite calculer I = \int_{0}^{\infty} \frac{\sin t}{t} d t .$ $(1) On d \overset{´}{e f i n i t} la fonction F (x) = \int_{0}^{\infty} e^{- t x} \frac{\sin t}{t} d t .$ $(a) D \overset{´}{e t e r m i n e r} le domaine de d \overset{´}{e f i n i t i o n} de f sur R .$ $(b) Montrer que F est de classe C^{1} sur R_{+}^{*} et calculer F^{'} (x) .$ $(c) Limite de F en + \infty ? Cons \overset{´}{e q u e n c e} ?$ $(2) On note S i (t) = \int_{0}^{t} \frac{\sin u}{u} d u pour tout r \overset{´}{e e l} t .$ $(a) Montrer que G (x) = \int_{0}^{\infty} e^{- t x} S i (t) d t est d \overset{´}{e f i n i e} sur R_{+}^{*} .$ $(b) Montrer que x G (x) \to I quand x \to 0^{+} .$ $(c) Au moyen d^{'} une int \overset{´}{e g r a t i o n} par parties, montrer que F est continue en 0 .$ $(3) Calculer I .$

Question Number 144721 Answers: 0 Comments: 0

......... Nice ......∗∗∗......Calculus......... f ( x ) : = [ tan (x) + cot (x) ] R_( f ) = ? Hint:: [ x ] := Max { m ∈Z ∣ m ≤ x }

$. . . . . . . . . Nice . . . . . . * * * . . . . . . Calculus . . . . . . . . .$ $f (x) : = [\tan (x) + \cot (x)]$ $R_{f} = ?$ $Hint :: [x] := Max {m \in Z ∣ m ⩽ x}$

Question Number 144720 Answers: 1 Comments: 0

.....calculus..... Ω := ∫_0 ^( ∞) ((sech(πx))/(1+4x^( 2) )) dx =^? (1/2) Ln(2)

$. . . . . calculus . . . . .$ $Ω := \int_{0}^{\infty} \frac{s e c h (π x)}{1 + 4 x^{2}} d x \overset{?}{=} \frac{1}{2} Ln (2)$

Question Number 144705 Answers: 1 Comments: 0

∫ (x^(n−1) /(x^(3n+1) (x^n −a))) dx ?

$\int \frac{x^{n - 1}}{x^{3 n + 1} (x^{n} - a)} dx ?$

Question Number 144691 Answers: 1 Comments: 0

Question Number 144662 Answers: 1 Comments: 0

........... Calculus........... In AB^Δ C : B^ = 2 C^ , a = λ b then specify the limits of the changes ′ λ ′ :

$. . . . . . . . . . . Calculus . . . . . . . . . . .$ $In A \overset{Δ}{B C} :$ $\hat{B} = 2 \hat{C}, a = λ b t h e n s p e c i f y$ $t h e l i m i t s o f t h e c h a n g e s^{'} λ^{'} :$

Question Number 144638 Answers: 1 Comments: 0

Triangle AOC inscribed in the region cut from the parabola y=x^2 by the line y=a^2 .Find the limit of ratio of the area of the triangle to the area of the parabolic region as a approaches zero

$Triangle AOC inscribed$ $in the region cut from$ $the parabola y = x^{2} by the$ $line y = a^{2} . Find the limit$ $of ratio of the area of the$ $triangle to the area of the$ $parabolic region as a approaches$ $zero$